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%I #14 Oct 10 2023 05:11:31
%S 1,1,5,25,135,775,4651,28845,183450,1190050,7844230,52389678,
%T 353770190,2411324700,16568343325,114639216915,798076174113,
%U 5586035989185,39287407321075,277508001643575,1967816928168265,14003018984540741,99965175670335750
%N G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^(5/2).
%F a(n) = Sum_{k=0..n} binomial(n+3*k/2-1,n-k) * binomial(5*k/2,k) / (3*k/2+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n+3*k/2-1, n-k)*binomial(5*k/2, k)/(3*k/2+1));
%Y Partial sums give A366400.
%Y Cf. A006319, A071724, A213282, A213336, A366432, A366433, A366434, A366435, A366436, A366437.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 09 2023